A Differential game approach in the case of a polluting oligopoly

In this paper we propose an oligopolistic market model of pollution, where demand is not linear and firms are revenue maximizers. Additionally we assume that the rate of purification is very small tending to zero and that each firm accumulates a pollution share depending for example on firm’s size. The game ends up with Markov strategies employed by all firms. Our findings show that under conditions it is possible a marginal decrease on the total pollution stock to increase firms’ discounted revenues. A reallocation caused by a uniform decrease in all firms pollution, reorders the marginal change of the pollution stocks in reverse of the original order of the allowed pollution